1. Field of the Invention
This invention relates to a method for estimating a cardiovascular or hemodynamic parameter such as cardiac output (CO), as well as to a system that implements the method.
2. Background Art
Cardiac output (CO) is an important indicator not only for diagnosis of disease, but also for continuous monitoring of the condition of both human and animal subjects, including patients. Few hospitals are therefore without some form of conventional equipment to monitor cardiac output.
One basis for most common CO-measurement systems is the well-known formula CO=HR·SV, where SV is the stroke volume and HR is the heart rate. SV is usually measured in liters and HR is usually measured in beats per minute, although any other units of volume and time may be used. This formula simply expresses that the amount of blood the heart pumps out over a unit of time (such as a minute) is equal to the amount it pumps out on every beat (stroke) times the number of beats per time unit.
Since HR is easy to measure using any of a wide variety of instruments, the calculation of CO usually depends on some technique for estimating SV. Conversely, any method that directly yields a value for CO can be used to determine SV by division by HR. Of course, estimates of CO or SV can then be used to estimate, or contribute to estimating, any parameter that can be derived from either of these values.
One invasive way to determine cardiac output (or, equivalently, SV) is to mount some flow-measuring device on a catheter, and then to thread the catheter into the subject and to maneuver it so that the device is in or near the subject's heart. Some such devices inject either a bolus of material or energy (usually heat) at an upstream position, such as in the right atrium, and determine flow based on the characteristics of the injected material or energy at a downstream position, such as in the pulmonary artery. Patents that disclose implementations of such invasive techniques (in particular, thermodilution) include:
U.S. Pat. No. 4,236,527 (Newbower et al., 2 Dec. 1980);
U.S. Pat. No. 4,507,974 (Yelderman, 2 Apr. 1985);
U.S. Pat. No. 5,146,414 (McKown, et al., 8 Sep. 1992); and
U.S. Pat. No. 5,687,733 (McKown, et al., 18 Nov. 1997).
Still other invasive devices are based on the known Fick technique, according to which CO is calculated as a function of oxygenation of arterial and mixed venous blood. In most cases, oxygenation is sensed using right-heart catheterization. There have, however, also been proposals for systems that measure arterial and venous oxygenation non-invasively, in particular, using multiple wavelengths of light, but to date they have not been accurate enough to allow for satisfactory CO measurement on actual patients.
Invasive techniques have obvious disadvantages, the main one of which is of course that catheterization of the heart is potentially dangerous, especially considering that the subjects (especially intensive care patients) on which it is performed are often already in the hospital because of some actually or potentially serious condition. Invasive methods also have less obvious disadvantages: Some techniques such as thermodilution rely on assumptions, such as uniform dispersion of the injected heat, that affect the accuracy of the measurements depending on how well they are fulfilled. Moreover, the very introduction of an instrument into the blood flow may affect the value (for example, flow rate) that the instrument measures.
There has therefore been a long-standing need for some way of determining CO that is both non-invasive—or at least as minimally invasive as possible—and accurate. One blood characteristic that has proven particularly promising for accurately determining CO non-invasively is blood pressure.
Most known blood-pressure-based systems rely on the so-called pulse contour method (PCM), which calculates an estimate of CO from characteristics of the beat-to-beat pressure waveform. In the PCM, “Windkessel” (German for “air chamber”) parameters (characteristic impedance of the aorta, compliance, and total peripheral resistance) are used to construct a linear or non-linear, hemodynamic model of the aorta. In essence, blood flow is analogized to a flow of electrical current in a circuit in which an impedance is in series with a parallel-connected resistance and capacitance (compliance).
FIG. 1 illustrates a classic two-element Windkessel model, in which Q(t) is the flow of blood from the heart to the aorta (or pulmonary artery); P(t) is the blood pressure in the aorta (or pulmonary artery) at time t; C is arterial compliance; and R is peripheral resistance in the systemic (or pulmonary) arterial system, all in suitable units. Assuming that the entire flow Q(t)=Q is constant and takes place only during systole, one obtains the following expression for P(t) during systole:P(t)=R·Q−(R·Q−Ped)·et/τ  (Equation 1)where Ped is the end-diastolic pressure (diastolic pressure) and τ=R·C is a decay constant. During diastole, Q(t)=0 (no inflow) and the expression for P(t) reduces to:P(t)=Pese−t/τ  (Equation 2)where Pes is the end-systolic pressure.
The three required parameters of the model are usually determined either empirically, through a complex calibration process, or from compiled “anthropometric” data, that is, data about the age, sex, height, weight, etc., of other patients or test subjects. U.S. Pat. No. 5,400,793 (Wesseling, 28 Mar. 1995) and U.S. Pat. No. 5,535,753 (Petrucelli, et al., 16 Jul. 1996) are representative of systems that rely on a Windkessel circuit model to determine CO.
Many extensions to the simple two-element Windkessel model have been proposed in hopes of better accuracy. One such extension was developed by the Swiss physiologists Broemser and Ranke in their 1930 article “Ueber die Messung des Schlagvolumens des Herzens auf unblutigem Weg,” Zeitung für Biologie 90 (1930) 467-507. FIG. 2 illustrates this model. In essence, the Broemser model—also known as a three-element Windkessel model—adds a third element (shown as resistance R0) to the basic two-element Windkessel model to simulate resistance to blood flow due to the aortic or pulmonary valve. It can be shown that the Broemser model reduces to the basic two-element Windkessel model under either of two circumstances: 1) R0=0; and 2) at diastole, when Q(t)=0 and dQ(t)/dt=0. Windkessel models having even more elements than three have also been proposed and analyzed.
PCM-based systems can monitor CO more or less continuously, with no need for a catheter to be left in the patient. Indeed, some PCM systems operate using blood pressure measurements taken using a finger cuff. One drawback of PCM, however, is that it is no more accurate than the rather simple, three-parameter model from which it is derived; in general, a model of a much higher order would be needed to faithfully account for other phenomena, such as the complex pattern of pressure wave reflections due to multiple impedance mis-matches caused by, for example, arterial branching. Other improvements have therefore been proposed, with varying degrees of complexity.
The “Method and Apparatus for Measuring Cardiac Output” disclosed by Salvatore Romano in U.S. Pat. No. 6,758,822, for example, represents a different attempt to improve upon PCM techniques by estimating SV, either invasively or non-invasively, as a function of the ratio between the area under the entire pressure curve and a linear combination of various components of impedance. In attempting to account for pressure reflections, the Romano system relies not only on accurate estimates of inherently noisy derivatives of the pressure function, but also on a series of empirically determined, numerical adjustments to a mean pressure value.
U.S. Published Patent Application No. 2004 0158163 (Richard J. Cohen, et al., 12 Aug. 2004, “Methods and apparatus for determining cardiac output”) describes yet another technique for determining CO from the pulse pressure profile P(t). According to Cohen's method, the arterial blood pressure waveform (time profile) P(t) is measured over more than one cardiac cycle. For example, assume a pressure measurement taken over three cardiac cycles. The area under the pressure curve is then computed for each cardiac cycle. The pressure profile P(t) is also sampled (“digitized”) to form a sequence of discrete values y(j) that represent P(t).
As is well known, the impulse response of any system is the function that describes how it acts (in reality or in a theoretical model) when it is subjected to an impulse of energy, force, etc. One step of Cohen's method involves creating a sequence of impulses x(k)—one at the beginning of each cardiac cycle—that has the same area as the “arterial pulse pressure.” A second embodiment of Cohen's method involves creating a sequence of impulses x(k), each, of which is located at the beginning of each cardiac cycle, with impulses that have equal areas but that are independent of the areas of the corresponding arterial pulse pressure waveforms. The values of x(k) and y(j) are then used in a convolution computation that models the cardiac system thus:
                              y          ⁡                      (            k            )                          =                                            ∑                              i                =                1                            m                        ⁢                                          a                i                            ·                              y                ⁡                                  (                                      k                    -                    i                                    )                                                              +                                    ∑                              i                =                1                            n                        ⁢                                          b                i                            ·                              x                ⁡                                  (                                      k                    -                    i                                    )                                                              +                      e            ⁡                          (              k              )                                                          (                  Equation          ⁢                                          ⁢          3                )            where e(t) is the residual error term, and m and n limit the number of terms in the model. The set of coefficients {ai, bi} that optimizes the equation is then determined, for example, over 60-90 second intervals of x(k) and y(j), and by using least-squares optimization to minimize the residual error term e(t).
Given ai and bi, Cohen then derives a single impulse response function h(t) that covers the entire multi-cycle measurement interval. It has long been known that the impulse response function of the heart usually takes the form, approximately, of a first-order exponential decay function. After an initial “settling” time of about 1.5-2.0 seconds, after which the effects of pressure reflections have mostly died out, Cohen then approximates h(t) from the expression:
                              h          ⁡                      (            t            )                          =                              A            ⁢                                                  ⁢                          ⅇ                                                -                  t                                                  τ                  D                                                              +                      w            ⁡                          (              t              )                                                          (                  Equation          ⁢                                          ⁢          4                )            The parameters A (an assumed amplitude) and TD (the time constant) are then estimated from a minimization of the residual weight function w(t).
Cohen then computes CO, for example, from some variant of the formula:CO=AC*ABP/τD  (Equation 5)where AC is a scaling constant and ABP is “arterial blood pressure,” usually the average arterial blood pressure. The scaling factor AC can be determined using an independent calibration, and will either be, or at least be related to the arterial compliance value C. This is because, as is known:CO=MAP/R  (Equation 6)where MAP is the mean arterial pressure, which in most cases will be the same as Cohen's term ABP. Equation 5 transforms into Equation 6 if AC=C, since τD=R*C.
One weaknesses of the approach disclosed by Cohen is that it requires determination of the scaling, that is, calibration factor AC, or, equivalently, determination of C. Accuracy of the CO measurement is therefore closely dependent on the accuracy of the calibration or compliance calculation. Another weakness of Cohen's method is that the recursive expression (Equation 3) used assumes a constant input amplitude and therefore fails to determine the proper d.c. offset. This in turn causes an even greater reliance on accurate determination of AC (or C).
Still another disadvantage of Cohen's approach is that it ignores much of the information contained in the pressure waveform—indeed, one embodiment of Cohen's method uses only a single characteristic of each waveform, namely, the area, when constructing the impulses x(k). In a second embodiment of Cohen's method, the information contained in the pulse pressure waveform is totally ignored. Cohen compensates for this in part by evaluating many pressure waveforms at a time—for example, Cohen's preferred embodiment monitors CO by analyzing “long time scale variations (greater than a cardiac cycle) in a single ABP signal” and determines τD “through the analysis of long time intervals” 60-90 seconds long. Another consequence of Cohen's greatly simplified input signal x(t) is the need for a complicated transfer function model (see Equation 3), which involves many zeroes, many poles, and, consequently, design and computational complexity.
What is needed is a system and method of operation for estimating CO, or any parameter that can be derived from or using CO, that is robust and accurate and that is less sensitive to calibration errors. This invention meets this need, and, indeed, provides an advantageous method and system for estimating even other cardiovascular parameters.